Solution to problem 13.1.19 from the collection of Kepe O.E.

13.1.19

Given: a material point M with a mass of 1.2 kg moves in a circle of radius r = 0.6 m according to the equation s = 2.4t.

Find: the modulus of the resultant forces applied to a material point.

Answer:

Initially, it is necessary to find the speed of the material point. According to the formula for uniformly rectilinear motion, the speed can be expressed as v = s/t. In the case of corresponding circular motion, it is necessary to use the speed formula v = 2πr/T, where T is the period of motion.

The period of motion can be found by knowing the dependence of the path s on time t: s = 2πr(t/T). It follows that T = 2πr/v = 2πr/2πr/T, i.e. T = s/v.

Thus, v = 2πr/T = 2πr/(s/v) = v²s/(2πr).

From the equation of motion s = 2.4t it follows that v = ds/dt = 2.4 m/s.

The acceleration of the material point in this case is centripetal and is equal to a = v²/r = 2.4²/0.6 = 9.6 m/s².

The modulus of the resultant forces F can be found using the well-known formula F = ma, where m is the mass of the material point. Thus, F = 1.2 kg * 9.6 m/s² = 11.5 N.

Answer: 11.5.

Solution to problem 13.1.19 from the collection of Kepe O..

This digital product is a solution to problem 13.1.19 from a collection of physics problems for secondary school students, compiled by O. Kepe. The solution contains a detailed description of each step necessary to obtain the final answer, as well as the formulas and calculations used to solve the problem.

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Problem 13.1.19 from the collection of problems by Kepe O.?. consists in determining the modulus of the resultant force acting on a material point with a mass of 1.2 kg moving in a circle of radius 0.6 meters, if its coordinate changes according to the law s = 2.4t. To solve the problem, it is necessary to calculate the speed of the material point, then determine the centripetal acceleration and, finally, the resultant force. The solution to the problem shows how to apply the laws of mechanics to simple movements in a circular path. The answer to the problem is 11.5.

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